Overview
Key data
| Item | Detail |
|---|---|
| Completed | c. 1st century (Eastern Han), compiled from earlier Qin and Han works |
| Structure | Nine chapters, 246 problems |
| Form | Each problem with its question, answer and method |
| Predecessor | Follows the “Book of Numbers” from the Zhangjiashan Han slips |
The contents of the nine chapters
The work is divided into nine chapters — rectangular fields, millet and rice, proportional division, diminishing breadth, consultation on works, equitable transport, excess and deficit, the rectangular array, and the right triangle —
each problem with its question, answer and method.
Its structure follows the “Book of Numbers” from the Zhangjiashan Han slips, but its system is more complete and its problems more numerous.
Its link with the calendar
The fractions, common denominators, proportions and methods of excess and deficit on which calendrical computation depends
all appear in its chapters.
New moons, intercalary remainders and grand epochs cannot be computed without arithmetic of this kind.
That the Chinese joined “calendar” and “calculation” in one phrase rests on this.
Value
The Nine Chapters is the backbone of ancient Chinese mathematics;
the mathematical works of the following thousand years developed within its frame.
Liu Hui is the most famous of its commentators, and his commentary is a classic of Chinese mathematics alongside the text itself.
Compiled and arranged by Chujia Kuang.